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Simplifying (x + -1)(x + -2)(x + -3)(x + -4) = (x + 1)(x + 2)(x + 3)(x + 4) Reorder the terms: (-1 + x)(x + -2)(x + -3)(x + -4) = (x + 1)(x + 2)(x + 3)(x + 4) Reorder the terms: (-1 + x)(-2 + x)(x + -3)(x + -4) = (x + 1)(x + 2)(x + 3)(x + 4) Reorder the terms: (-1 + x)(-2 + x)(-3 + x)(x + -4) = (x + 1)(x + 2)(x + 3)(x + 4) Reorder the terms: (-1 + x)(-2 + x)(-3 + x)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) Multiply (-1 + x) * (-2 + x) (-1(-2 + x) + x(-2 + x))(-3 + x)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) ((-2 * -1 + x * -1) + x(-2 + x))(-3 + x)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) ((2 + -1x) + x(-2 + x))(-3 + x)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) (2 + -1x + (-2 * x + x * x))(-3 + x)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) (2 + -1x + (-2x + x2))(-3 + x)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) Combine like terms: -1x + -2x = -3x (2 + -3x + x2)(-3 + x)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) Multiply (2 + -3x + x2) * (-3 + x) (2(-3 + x) + -3x * (-3 + x) + x2(-3 + x))(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) ((-3 * 2 + x * 2) + -3x * (-3 + x) + x2(-3 + x))(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) ((-6 + 2x) + -3x * (-3 + x) + x2(-3 + x))(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) (-6 + 2x + (-3 * -3x + x * -3x) + x2(-3 + x))(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) (-6 + 2x + (9x + -3x2) + x2(-3 + x))(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) (-6 + 2x + 9x + -3x2 + (-3 * x2 + x * x2))(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) (-6 + 2x + 9x + -3x2 + (-3x2 + x3))(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) Combine like terms: 2x + 9x = 11x (-6 + 11x + -3x2 + -3x2 + x3)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) Combine like terms: -3x2 + -3x2 = -6x2 (-6 + 11x + -6x2 + x3)(-4 + x) = (x + 1)(x + 2)(x + 3)(x + 4) Multiply (-6 + 11x + -6x2 + x3) * (-4 + x) (-6(-4 + x) + 11x * (-4 + x) + -6x2 * (-4 + x) + x3(-4 + x)) = (x + 1)(x + 2)(x + 3)(x + 4) ((-4 * -6 + x * -6) + 11x * (-4 + x) + -6x2 * (-4 + x) + x3(-4 + x)) = (x + 1)(x + 2)(x + 3)(x + 4) ((24 + -6x) + 11x * (-4 + x) + -6x2 * (-4 + x) + x3(-4 + x)) = (x + 1)(x + 2)(x + 3)(x + 4) (24 + -6x + (-4 * 11x + x * 11x) + -6x2 * (-4 + x) + x3(-4 + x)) = (x + 1)(x + 2)(x + 3)(x + 4) (24 + -6x + (-44x + 11x2) + -6x2 * (-4 + x) + x3(-4 + x)) = (x + 1)(x + 2)(x + 3)(x + 4) (24 + -6x + -44x + 11x2 + (-4 * -6x2 + x * -6x2) + x3(-4 + x)) = (x + 1)(x + 2)(x + 3)(x + 4) (24 + -6x + -44x + 11x2 + (24x2 + -6x3) + x3(-4 + x)) = (x + 1)(x + 2)(x + 3)(x + 4) (24 + -6x + -44x + 11x2 + 24x2 + -6x3 + (-4 * x3 + x * x3)) = (x + 1)(x + 2)(x + 3)(x + 4) (24 + -6x + -44x + 11x2 + 24x2 + -6x3 + (-4x3 + x4)) = (x + 1)(x + 2)(x + 3)(x + 4) Combine like terms: -6x + -44x = -50x (24 + -50x + 11x2 + 24x2 + -6x3 + -4x3 + x4) = (x + 1)(x + 2)(x + 3)(x + 4) Combine like terms: 11x2 + 24x2 = 35x2 (24 + -50x + 35x2 + -6x3 + -4x3 + x4) = (x + 1)(x + 2)(x + 3)(x + 4) Combine like terms: -6x3 + -4x3 = -10x3 (24 + -50x + 35x2 + -10x3 + x4) = (x + 1)(x + 2)(x + 3)(x + 4) Reorder the terms: 24 + -50x + 35x2 + -10x3 + x4 = (1 + x)(x + 2)(x + 3)(x + 4) Reorder the terms: 24 + -50x + 35x2 + -10x3 + x4 = (1 + x)(2 + x)(x + 3)(x + 4) Reorder the terms: 24 + -50x + 35x2 + -10x3 + x4 = (1 + x)(2 + x)(3 + x)(x + 4) Reorder the terms: 24 + -50x + 35x2 + -10x3 + x4 = (1 + x)(2 + x)(3 + x)(4 + x) Multiply (1 + x) * (2 + x) 24 + -50x + 35x2 + -10x3 + x4 = (1(2 + x) + x(2 + x))(3 + x)(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = ((2 * 1 + x * 1) + x(2 + x))(3 + x)(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = ((2 + 1x) + x(2 + x))(3 + x)(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = (2 + 1x + (2 * x + x * x))(3 + x)(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = (2 + 1x + (2x + x2))(3 + x)(4 + x) Combine like terms: 1x + 2x = 3x 24 + -50x + 35x2 + -10x3 + x4 = (2 + 3x + x2)(3 + x)(4 + x) Multiply (2 + 3x + x2) * (3 + x) 24 + -50x + 35x2 + -10x3 + x4 = (2(3 + x) + 3x * (3 + x) + x2(3 + x))(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = ((3 * 2 + x * 2) + 3x * (3 + x) + x2(3 + x))(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = ((6 + 2x) + 3x * (3 + x) + x2(3 + x))(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = (6 + 2x + (3 * 3x + x * 3x) + x2(3 + x))(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = (6 + 2x + (9x + 3x2) + x2(3 + x))(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = (6 + 2x + 9x + 3x2 + (3 * x2 + x * x2))(4 + x) 24 + -50x + 35x2 + -10x3 + x4 = (6 + 2x + 9x + 3x2 + (3x2 + x3))(4 + x) Combine like terms: 2x + 9x = 11x 24 + -50x + 35x2 + -10x3 + x4 = (6 + 11x + 3x2 + 3x2 + x3)(4 + x) Combine like terms: 3x2 + 3x2 = 6x2 24 + -50x + 35x2 + -10x3 + x4 = (6 + 11x + 6x2 + x3)(4 + x) Multiply (6 + 11x + 6x2 + x3) * (4 + x) 24 + -50x + 35x2 + -10x3 + x4 = (6(4 + x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) 24 + -50x + 35x2 + -10x3 + x4 = ((4 * 6 + x * 6) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) 24 + -50x + 35x2 + -10x3 + x4 = ((24 + 6x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) 24 + -50x + 35x2 + -10x3 + x4 = (24 + 6x + (4 * 11x + x * 11x) + 6x2 * (4 + x) + x3(4 + x)) 24 + -50x + 35x2 + -10x3 + x4 = (24 + 6x + (44x + 11x2) + 6x2 * (4 + x) + x3(4 + x)) 24 + -50x + 35x2 + -10x3 + x4 = (24 + 6x + 44x + 11x2 + (4 * 6x2 + x * 6x2) + x3(4 + x)) 24 + -50x + 35x2 + -10x3 + x4 = (24 + 6x + 44x + 11x2 + (24x2 + 6x3) + x3(4 + x)) 24 + -50x + 35x2 + -10x3 + x4 = (24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4 * x3 + x * x3)) 24 + -50x + 35x2 + -10x3 + x4 = (24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4x3 + x4)) Combine like terms: 6x + 44x = 50x 24 + -50x + 35x2 + -10x3 + x4 = (24 + 50x + 11x2 + 24x2 + 6x3 + 4x3 + x4) Combine like terms: 11x2 + 24x2 = 35x2 24 + -50x + 35x2 + -10x3 + x4 = (24 + 50x + 35x2 + 6x3 + 4x3 + x4) Combine like terms: 6x3 + 4x3 = 10x3 24 + -50x + 35x2 + -10x3 + x4 = (24 + 50x + 35x2 + 10x3 + x4) Add '-24' to each side of the equation. 24 + -50x + 35x2 + -10x3 + -24 + x4 = 24 + 50x + 35x2 + 10x3 + -24 + x4 Reorder the terms: 24 + -24 + -50x + 35x2 + -10x3 + x4 = 24 + 50x + 35x2 + 10x3 + -24 + x4 Combine like terms: 24 + -24 = 0 0 + -50x + 35x2 + -10x3 + x4 = 24 + 50x + 35x2 + 10x3 + -24 + x4 -50x + 35x2 + -10x3 + x4 = 24 + 50x + 35x2 + 10x3 + -24 + x4 Reorder the terms: -50x + 35x2 + -10x3 + x4 = 24 + -24 + 50x + 35x2 + 10x3 + x4 Combine like terms: 24 + -24 = 0 -50x + 35x2 + -10x3 + x4 = 0 + 50x + 35x2 + 10x3 + x4 -50x + 35x2 + -10x3 + x4 = 50x + 35x2 + 10x3 + x4 Add '-35x2' to each side of the equation. -50x + 35x2 + -10x3 + -35x2 + x4 = 50x + 35x2 + 10x3 + -35x2 + x4 Reorder the terms: -50x + 35x2 + -35x2 + -10x3 + x4 = 50x + 35x2 + 10x3 + -35x2 + x4 Combine like terms: 35x2 + -35x2 = 0 -50x + 0 + -10x3 + x4 = 50x + 35x2 + 10x3 + -35x2 + x4 -50x + -10x3 + x4 = 50x + 35x2 + 10x3 + -35x2 + x4 Reorder the terms: -50x + -10x3 + x4 = 50x + 35x2 + -35x2 + 10x3 + x4 Combine like terms: 35x2 + -35x2 = 0 -50x + -10x3 + x4 = 50x + 0 + 10x3 + x4 -50x + -10x3 + x4 = 50x + 10x3 + x4 Add '-1x4' to each side of the equation. -50x + -10x3 + x4 + -1x4 = 50x + 10x3 + x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -50x + -10x3 + 0 = 50x + 10x3 + x4 + -1x4 -50x + -10x3 = 50x + 10x3 + x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -50x + -10x3 = 50x + 10x3 + 0 -50x + -10x3 = 50x + 10x3 Solving -50x + -10x3 = 50x + 10x3 Solving for variable 'x'. Reorder the terms: -50x + -50x + -10x3 + -10x3 = 50x + 10x3 + -50x + -10x3 Combine like terms: -50x + -50x = -100x -100x + -10x3 + -10x3 = 50x + 10x3 + -50x + -10x3 Combine like terms: -10x3 + -10x3 = -20x3 -100x + -20x3 = 50x + 10x3 + -50x + -10x3 Reorder the terms: -100x + -20x3 = 50x + -50x + 10x3 + -10x3 Combine like terms: 50x + -50x = 0 -100x + -20x3 = 0 + 10x3 + -10x3 -100x + -20x3 = 10x3 + -10x3 Combine like terms: 10x3 + -10x3 = 0 -100x + -20x3 = 0 Factor out the Greatest Common Factor (GCF), '-20x'. -20x(5 + x2) = 0 Ignore the factor -20.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + x2)' equal to zero and attempt to solve: Simplifying 5 + x2 = 0 Solving 5 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 0 + -5 x2 = 0 + -5 Combine like terms: 0 + -5 = -5 x2 = -5 Simplifying x2 = -5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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